ENDOGENOUS DEMAND IN SUPPLY CHAIN NETWORK DESIGN

Transcription

1 ENDOGENOUS DEMAND IN SUPPLY CHAIN NETWORK DESIGN BEN LILLIJORD AND ALAN LI MIT SCM CAPSTONE PROJECT

2 AGENDA Introduction Methodology Analysis Conclusion Motivation Cost minimization vs profit maximization Model outline Endogenous demand incarnations Sensitivity analysis Results Summary Future Research

3 INTRODUCTION MOTIVATION LOOKING BEYOND COSTS What happens when a new facility opens? 1. Costs incurred 2. Costs saved Any change in revenue? 1. Better service 2. Brand recognition Cost Revenue Profit

4 INTRODUCTION MOTIVATION PROFIT MAXIMIZATION Cost Minimization Profit Maximization Finds low-cost network to meet expected demand Considers only costs Revenue generation is incidental Demand changes depending on network design (Endogenous Demand) Considers costs and revenues Revenue generation is optimized

5 ANALYSIS STEP FUNCTION ENDOGENOUS Simplest endogenous model Represents same-day shipping Demand increases by a set amount for customers near the facility

6 METHODOLOGY OBJECTIVE FUNCTIONS & CONSTRAINTS Objective Functions Cost minimization objective function: Profit maximization objective function:! % " & " +!! ) "( (+ "( )- "(.!! / "( ) "( + "( - "(! % " & ". "#$ "#$ (#$ "#$ (#$ "#$ Facility Fixed Cost Delivery Cost Capacity constraint Revenue per unit Linking constraint Common Constraints! - "( 9 ", : ;. ( Binary constraint for facilities: & " = {0, } 1, : ;.! - "( <& ", : ;. ( All flow of product must be non-negative: - "( 0, : ;, 5 7. Demand Constraints Traditional demand:! - "( 2 (, 5 7. " Endogenous demand! - "( 2 ( +! C2 "( + "(, 5 7. " "

7 METHODOLOGY ENDOGENOUS DEMAND EFFECT FUNCTION & COEFFICIENT The general form of the endogenous demand effect function:! " $% "& (( "& # =! " * & + " $ "& (( "& )- "& % &, 0 2. Quadratic Form The endogenous demand constraint becomes:! " 1 * & + " $ "& (( "& # % & - "& % &, 0 2. Endogenous Demand Coefficient Where: * & is the variation of the demand from customer locations j, for 0 2. $ "& ( "& describes the endogenous effect incarnation.

8 METHODOLOGY VARIOUS ENDOGENOUS DEMAND COEFFICIENT! " 1 & ' ( " ) "' (+ "' %, ' - "', ', 1 3. ) "' + "' = 0 Traditional model (a)

9 METHODOLOGY VARIOUS ENDOGENOUS DEMAND COEFFICIENT! " 1 & ' ( " ) "' (+ "' %, ' - "', ', 1 3. ) "' + "' = 0 Traditional model (a) ) "' + "' = const. Step Endogenous model (b)

10 METHODOLOGY VARIOUS ENDOGENOUS DEMAND COEFFICIENT! " 1 & ' ( " ) "' (+ "' %, ' - "', ', 1 3. ) "' + "' = 0 Traditional model (a) ) "' + "' = const. Step Endogenous model (b) ) "' + "' <=> = 5 A B CD EB FGHIJFGIKL B FGHIJFGIKL 1, Exponential Endogenous model (c) v Product/industry specific function form available from regression of market research data

11 ANALYSIS SENSITIVITY ANALYSIS The analysis is performed in Python with IBM CPLEX Optimizer. Each combination of metrics was tested in a total of 40,320 runs and 1,260 optimal solutions in the sensitivity analysis alone. Assumptions Unconstrained capacity Step Endogenous Incarnation Focus on network design corresponding fixed cost and delivery (linehaul) cost Direct distance by using Haversine formula with longitude and latitude of each city Demand in each region is simplified to be concentrated and located in the city centroid Combination of matrices Fixed cost of an additional facility (values from $25,000 to $600,000). Variable per mile cost of shipping goods (values from $0.005 to $0.15). Total demand at each demand center (values from 2,000 to 20,000). Variable demand from endogenous effects (values from 300 to 1,500).

12 ANALYSIS ENDOGENOUS EXPRESSION VS FIXED COST OF FACILITY Probability Profit Margin Improvement

13 ANALYSIS ENDOGENOUS EXPRESSION VS COST PER UNIT MILE Probability Profit Margin Improvement

14 ANALYSIS ENDOGENOUS EXPRESSION VS TOTAL DEMAND Probability Profit Margin Improvement

15 ANALYSIS ENDOGENOUS EXPRESSION VS VARIABLE DEMAND Probability Profit Margin Improvement

16 ANALYSIS STEP FUNCTION ENDOGENOUS Profit increases as high as 10.2% Under favourable conditions, average profit increase of 3.2% More profitable network found in nearly half of the simulations at only 10% endogenous effect Complex networks tend to see greater benefits

17 ANALYSIS ENDOGENOUS EXPRESSION STEP FUNCTION Probability Profit Margin Improvement

18 ANALYSIS NETWORK EXPANSION PROBLEM Common problem: decision to add one or more facilities Average Return On Assets increased by 10% with profit maximizing model Promotes faster network expansion The profit maximization model often chose locations that were never chosen by the cost minimization model

19 CONCLUSION SUMMARY OF RESULTS Three significant findings: 1. Even small endogenous effects result in network changes 2. The profit maximization model was more valuable in complex networks 3. Profit maximization model tends to place facilities closer to demand centers

20 CONCLUSION FUTURE RESEARCH Applications Perform demand analysis for specific industry to estimate potential for endogenous effect and model incarnation Capacitated facility study Use the uncapacitated model in this thesis as a basis, future research can work on capacitated problem Distance for route between each pair of facility and client Change the direct distance by using Haversine formula with longitude and latitude to real route with google map API

21 THANK YOU QUESTIONS? Ben Lillijord Bachelor of Science Mechanical Engineering University of Alberta Alan Li Master of Science Applied Mechanics National Taiwan University